Compressible Euler limit from Boltzmann equation with complete diffusive boundary condition in half-space

Abstract

In this paper, we prove the compressible Euler limit from the Boltzmann equation with hard sphere collisional kernel and complete diffusive boundary condition in half-space by employing the Hilbert expansion which includes interior and Knudsen layers. This rigorously justifies the corresponding formal analysis in Sone's book \cite{Sone-2007-Book} in the context of short time smooth solutions, and also generalizes the classic Caflisch's result \cite{Caflish-1980-CPAM} to initial-boundary problem case.

32 pages. arXiv admin note: text overlap with arXiv:2101.11199